Gah, I haven't really thought of this, despite writing a next-gen fic because I've only been thinking about Sasuke.
(387 spoilers)
And if those spoilers in 387 turn out to be true, omg! Gotta change my story a bit...
I think Naruto would be the "fun" parent. The one where you ask him first if you want something because he's more likely to give into you. However, I
can see him doing the "ask your mother" thing that is the bane of children everywhere.
Sakura is definately the "bad cop" in the combo to me. On a slightly negative note, I think she will be sort of distant once she stops nursing her child(ren), just because I feel she'll probably have the busier schedule with being a medical-ninja. However, despite her schedule, she'll have people wondering how she can work, micro-manage her kids and stay sane.
As for babysitter, Iruka would be perfect! He's great with kids, and if he could survive Naruto, he can survive anyone, he's responsible, and he's dependable since as a teacher he's going to stay put. I think he might be godfather, if Sasuke isn't.
Sasuke? I think Naruto and Sakura would have to come to him, he wouldn't come to them. But I don't think he'd be babysitter. I can just see Sasuke getting sick of handling a bunch of hyper kids and tying them up somewhere while going off to training. I think they'll spare him the trouble.
Family Vacations? Naruto would probably get them lost on some random adventure of his, and everyone will b*tch, but in retrospect they'll realize that those detours were the the best moments they had together. I can't see them having many of them though, I think Naruto and Sakura will be pretty busy, and if their kids enter the ninja academy, it'll probably be impossible to just find the time.
That's all I got for now...